Factor the following expression: $3$ $x^2+$ $11$ $x$ $-4$
Explanation: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(3)}{(-4)} &=& -12 \\ {a} + {b} &=& & & {11} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-12$ and add them together. Remember, since $-12$ is negative, one of the factors must be negative. The factors that add up to ${11}$ will be your ${a}$ and ${b}$ When ${a}$ is ${-1}$ and ${b}$ is ${12}$ $ \begin{eqnarray} {ab} &=& ({-1})({12}) &=& -12 \\ {a} + {b} &=& {-1} + {12} &=& 11 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {3}x^2 {-1}x +{12}x {-4} $ Group the terms so that there is a common factor in each group: $ ({3}x^2 {-1}x) + ({12}x {-4}) $ Factor out the common factors: $ x(3x - 1) + 4(3x - 1) $ Notice how $(3x - 1)$ has become a common factor. Factor this out to find the answer. $(3x - 1)(x + 4)$